Final answer:
Using the cosine of the angle of elevation, we calculate that the distance from the bottom of the ladder to the side of the house is approximately 4.1 ft, corresponding to Option A.
Step-by-step explanation:
To find the distance from the bottom of the ladder to the side of the house, we use trigonometric functions, specifically the cosine function for this right-angled triangle situation. The angle of elevation is given as 74°, and the height at which the ladder reaches the wall is 15 ft. Cosine relates the adjacent side (the distance we want to find) to the hypotenuse (the length of the ladder).
The cosine of 74° equals the adjacent side (distance from the house) over the hypotenuse (the ladder's length). So, the equation is cos(74°) = distance from the house / 15 ft. Rearranging to solve for the distance from the house yields: distance from the house = 15 ft * cos(74°). Calculating this gives approximately 4.056 ft, and rounding to the nearest tenth gives us 4.1 ft.
Therefore, the distance from the bottom of the ladder to the side of the house is 4.1 ft (Option A).